The subgroup

General facts

Here are some general facts about this subgroup.

Its normalizer is when is even. When is odd, is self-normalizing.

The conjugate subgroups to this subgroup are subgroups of the form . When is odd, this includes all subgroups of the form , whereas if is even, this includes only half the subgroups of the form . There are thus conjugate subgroups if is even and conjugate subgroups if is odd.

If ,there are three automorphic subgroups, . If , the automorphic subgroups to this subgroup are subgroups of the form . There are thus of them if .

The normal closure of is . This is the whole group if is odd and is a subgroup of index two if is even.